How does the self interaction of gravity (gravitons) shape spacetime? What's the quantum mechanism? Or a wave description?

(In a related thread I asked "How does the speed of light vary in the presence of a magnetic field. We concluded it did not, but that it does curve. Photons always move at "c". So here I am inquiring why space curves as that is what causes light to curve.)

From Lee Smolin's book, THE TROUBLE WITH PHYSICS, page 85:

So the answer apparently lies within a background independent quantum gravity formulation...perhaps loop quantum gravity. It MAY also be this question: How does a passing gravitational wave (or gravitons) change a Penrose spin network construct of spacetime? (Think of a geodesic dome, with integer value nodes for areas and interger value links for volumes.)

From the perspective of general relativity, an observer in gravitational free fall will not observe any curvature of spacetime...they observe their own local motion as a geodesic straight line. They "see" themselves as inertial, no forces evident. A distant observer stationary with respect to the gravitational source viewing that same event will also see motion along a geodesic but the geodesic is curved, reflecting acceleration of the test body.

And if I understand it correctly, a non inertial (accelerating observer) will see a different geodesic path, meaning a different acceleration, than either of the other two. This latter type is called an inertial acceleration denoting that an acceleration is observed because of the non inertial reference frame, and is independent of the physical characteristics of the "test body".
(via THE RIDDLE OF GRAVITATION, Peter Bergmann, a former student of Einstein)

Given these variations pinning down the physcial interaction might be difficult.

I am also confused with curved space time...Just because light curves does that mean space-time is curved?...Nikola Tesla has said about GR that "I hold that space cannot be curved, for the simple reason that it can have no properties. It might as well be said that God has properties. He has not, but only attributes and these are of our own making. Of properties we can only speak when dealing with matter filling the space. To say that in the presence of large bodies space becomes curved is equivalent to stating that something can act upon nothing. I, for one, refuse to subscribe to such a view"...

Photons, and everything else, like planets, try to go where time is least. Gravity curves spacetime because the photons or anything that has mass are seeking or are pulled toward a path of least time, which is a path of more gravity. Physicists have proven with atomic clocks and airplanes that gravity slows time. Clocks run slower at lower altitudes where gravity is stronger. Time is least (flows more slowly) where gravity is most.

The earth orbiting the sun has momentum which keeps it in orbit. If the earth's momentum were to stop, the earth would seek the path of least time, and be pulled straight into the sun! It would not follow a curved path to the sun if it does not have momentum.

1) Mass causes gravity.
2) Mass seeks or is pulled where time is least.
3) The larger the mass, the least time is.
4) spacetime is curved due to the curvature of the mass.
5) Without mass, time is not curved.
6) Without momentum near a mass, space is not curved.

The reason why time slows down as you approach the speed of light is because the mass increases(More mass means less time). The question I have is why does mass slow time?

This is my understanding of why gravity curves spacetime. Please correct me where I am wrong.

Massive objects take a path of greatest proper time or spacetime distance, and light takes a path of least (zero) spacetime distance, provided they are acted on by gravity alone. This is equivalent to the statement that objects take "straightest" or geodesic spacetime paths, provided they are acted on by gravity alone.

The time slowing down thing is usually for clocks that are not acted on by gravity alone. For example one may compare two clocks that are stationary relative to the surface of the earth. These clocks are not acted on by gravity alone, since they are prevented from falling freely by whatever is keeping them stationary. These clocks are not following spacetime geodesics.

@Denton: At the speed of light, length shrinks to zero and time stands still. At 99% the speed of light the object's length would be near 0 and would pass the earth before it had time to pull the earth into it.

@atyy: An atomic clock is a clock that uses the resonance frequencies of atoms as its resonator. According to Encyclopedia Britannica, the resonator is "regulated by the frequency of the microwave electromagnetic radiation emitted or absorbed by the quantum transition (energy change) of an atom or molecule." They have to constantly update the clocks on GPS satellites because they are running faster than clocks on the surface of the earth.

Einstein said that time slows down and mass increases as you approach the speed of light. Am I the only one who sees this relationship, or is my thinking curved, which could be possible. lol

From the perspective a distant outside inertial observer that's correct; from the perspective of the near light speed frame observer, all appears as normal locally, but the time dilation and length contraction are seen in the frame of the outside observer. Each sees the other as moving near "c".

Einstein said that time slows down and mass increases as you approach the speed of light. From the perspective of a distant outside inertial observer that's correct; from the perspective of the near light speed frame observer, all appears as normal locally, but the time dilation and length contraction are seen in the frame of the outside observer. Each sees the other as moving near "c". I agree with you Naty1.

Massive objects take a path of greatest proper time or spacetime distance, and light takes a path of least (zero) spacetime distance, provided they are acted on by gravity alone. I agree with you Naty1. The reason why light takes a path of least (zero) spacetime distance is because the frequency is very high and the wavelength is very short. If you increase the mass/energy you increase the frequency and the wavelength is shorter. Massive objects takes the path of greatest spacetime distance or proper time because the energy is not as high as light and hence a longer wavelength. The frequency simply describes the number of oscillations or cycles per second, while the term wavelength describes the distance between one wave and the next. Hence wavelength and frequency are inseparably intertwined: the higher the frequency the shorter the wavelength.

Planck's formula: E=hf where:
E is the energy of a single photon,
f is the photon's frequency,
h is Planck's constant,
Einstein's formula: E=mc2 where:
E is energy,
m is mass,
c2 is the speed of light squared,
hence, hf=mc2

thus showing that the mass of a photon is directly proportional to the frequency of the photon.
E=hf and E=mc2 so hf=mc2

Velocity-based time dilation and gravity-based time dilation are two separate effects, the fact that a clock is running very slow (in whatever coordinate system you choose to use, keep in mind that different coordinate systems disagree about an object's velocity and there is no single 'true' velocity) doesn't imply it is a strong source of gravity.

Clocks run slower at lower altitudes (orbits) where gravity is stronger. An atomic clock in the outer orbit of earth will run faster than an atomic clock in the inner orbit of the earth, both clocks will be free falling.

I don't know how to do this calculation. Usually the angular coordinates of the two clocks are set equal, but I think that's not true of free falling clocks in different radii. However the question doesn't seem like an insensible one to ask, and I'd be curious to know the answer.

Yes: That's what general relativity states via the Einstein stress-energy tensor.

I'll bet you don't know what "nothing" means: ....(not many do; I don't) Spacetime is SOMETHING!!!!

But the important point is that even empty space ("nothing" to some people) has quantum fluctuations, zero point energy, and maybe dark energy and dark matter. And of course no space is empty because probability waves from other portions of the universe, cosmic background radiation, gravitational fields, cosmic rays, permeate everywhere...

I even looked up "nothing" for you on Wiki: here is how they describe NOTHING: (and I agree)

If you'd like to "see" what spacetime MAY look like, (no guarantees) research "Penrose spin networks"...spacetime appears as a geodesic shaped with edges equivalent to areas and nodes equivalent to volumes...at the roughly planck scale....

However, we all start off pretty much as you so don't despair..if you read Wiki on "Nothing" you'll have learned some good insights and make further progress each time you check out another aspect of physics....there are a LOT of pieces to our world...